Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

1961 IMO Problems/Problem 4

Revision as of 17:36, 6 April 2007 by Teki-Teki (talk | contribs) (posted problem from IMO Compendium)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

In the interior of triangle $ABC$ a point P is given. Let $Q_1,Q_2,Q_3$ be the intersections of $PP_1, PP_2,PP_3$ with the opposing edges of triangle $ABC$. Prove that among the ratios $\frac{PP_1}{PQ_1},\frac{PP_2}{PQ_2},\frac{PP_3}{PQ_3}$ there exists one not larger than 2 and one not smaller than 2.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1961_IMO_Problems/Problem_4&oldid=14412"